Supplementary Information for Charge-Induced Second-Harmonic Generation in Bilayer WSe Huakang Yu, Deep Talukdar, Weigao Xu, Jacob B. Khurgin,* and Qihua Xiong,3,* Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 63737 Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland 8, USA 3 NOVITAS, Nanoelectronics Centre of Excellence, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 * To whom correspondence should be addressed. Email address: Qihua@ntu.edu.sg and jakek@jhu.edu.
. Device characterization and ambipolar devices: 8 Intensity (a.u.) 6 4 S B E g A g 4 4 6 8 3 3 Raman shift (cm - ) Fig. S. Raman spectroscopy measurement for the bilayer WSe sample. The peaks at 7.8 cm - and 5.8 cm - correspond to the low frequency shear and breathing modes, while the high frequency peaks at 6 cm - and 39 cm - correspond to the inplane and out-of-plane modes. The laser excitation is 53-nm solid state laser with a power of. mw. I sd (µa) - -4-6 -4-4 V G (V) Fig. S. Transfer curve (I ds vs. V G ) of the bilayer WSe device. Semi-logarithmic (I ds -V G ) plot clearly illustrates the p-type behaviour of the FET. Inset shows a typical optical micrograph of the bilayer device with scale bar of 5 µm. Most of the transistors have p-type transport behaviour with a room-temperature current on-off ratio of 5 (see Fig. S). Using the parallel plate capacitor model, at a back gate voltage of -4 V and V th = - V the charge carrier concentration at -4 V can be estimated ~4.4 cm -. SHG spectra collected upon different gate bias are shown in Fig. S3. The integrated SHG intensities are used to estimate the chargeinduced second-order susceptibility plotted in Fig. b. For the ambipolar FETs obtained in different samples, we also performed the nonlinear optical experiments and found that CHISHG can be observed for both the electron and hole accumulations,
which is reasonable according to the bond-charge model (see Fig. S4). The ambipolar FET had nearly symmetric I-V G characteristics, caused by low unintentional doping - so form the nomenclature point of view one could see no difference between accumulation and deep inversion modes of operation. The SHG signal is repeatable and reproducible, the error bar of the charge induced χ () is small. SHG intensity (a.u.) 6 5 4 3 -V 55 53 535 54 Wavelength (nm) Fig. S3. SHG spectra recorded at different gate bias. It clearly indicates that increase in SHG signal followed by increasing biased gate. -4V -35V -3V -5V A I sd (µa) - -4-6 -4-4 V G (V) Charge-induced χ () (a.u.) B SHG intensity (a.u.) 3-4V V 4V 55 53 535 54 Wavelength (nm) Fig. S4. Charge-induced SHG from ambipolar bilayer WSe FET. (A) The transfer characteristics of a bilayer WSe device at V sd =- mv is shown. Note the current at the p-side is higher than in n-side by one order of magnitude. The blue dots represent the corresponding CISHG intensities recorded at different gate voltages. (B) SHG can be observed from the bilayer WSe sample with application of V G of -4 V and 4 V respectively. The spectra have been shifted vertically for clarity.. Bond picture of the valence band in the WSe layer and origin of chargeinduced χ () The 6 bonding orbitals per primitive cell have mixed ionic/covalent nature. Each Se atom contributes four outer shell 4p electrons while W atom contributes two 6s and two 5d electrons. The 6s orbitals have high energy and thus lose their electrons almost completely, contributing to the ionic character of bonding, while the lower lying 5d 3
orbitals make polar covalent bonds with Se 4p orbitals. For the most part it is 5d z orbital splits-off by the crystal field and hybridizes with Se 4 p z orbitals into the bonding orbitals. This simple bond-orbital picture describes the composition of the entire valence band. To explain the observed phenomena, we take a close look at the origin of monolayer WSe on the microscopic level (see Fig. 3A). Intuitively, () χ from () χ arises from the trigonal symmetry of the bonding orbitals between the W and Se atoms. From the above bond-orbital picture and energy dispersion relation (, ), one can see that the topmost states of the valence band located at the K-point, are composed almost exclusively from the tungsten 5d x y, xy orbitals which are tightly localized in x-y plane (Fig. a). Hence these orbits possess almost a complete lack of dispersion in the z direction and the charge density in these orbitals is akin to a very thin charge sheet. Mathematically, in this structure the third-order susceptibility tensor with out-of-plane (3) element (e.g., χ xxxz ) vanish which is supposed to be responsible for E-FISHG. 3. Electrostatic calculation for the accumulation charges in two W layers We consider a fully degenerate case (T = K) for a quantum well with one occupied subband. The gate potential can raise or lower the subband as accumulation/inversion layer capacitance given as, Cs = e D D, ( T = K), where DD is the constant of twodimensional density of states (D-DOS). The total accumulated charge above threshold is thus given by, Qi Cs ( VG VT ), for VG > VT. Now looking at Fig. 3D in the main text, simple electrostatic calculations leads us toward a simple relation between the accumulation charges in two W layers, Q = Q ( + e ρ t / ε ε ) () D W where dielectric constant ε W = 5., the difference between two W layers t =.3 nm, and ρ / π D = mv h is the D-DOS (factor is for two-fold K-point degeneracy). With effective mass mv =.56m we obtain Q.4Q, indicating that that the compensation is weak. 4. Estimation of effective heteropolar potential for WSe 4
Since there is no effective heteropolar potential value available for WSe, we decide to estimate it by comparing it with GaAs. Experimental data and theoretical calculations estimate the () χ of WSe to be comparable with that of GaAs (3). Given that () χ is proportional to the heteropolar potential of bonds, cube bond length and volume density of bonds, we can estimate the effective heteropolar potential for WSe by comparing with GaAs, i.e., l B, GaAs B, GaAs CWSe C.83 GaAs ev l B, WSe N B, WSe 3 N () where C 4.3 ev is estimated from ref. (4); N B, GaAs represents the volume density of GaAs GaAs with the value of.3 /Å 3 ; N B, WSe represents the volume density of WSe with the value of.33 /Å 3 ; l B, GaAs is the bond length of GaAs with the value of a 3 / /4 =.4 Å (a = 5.65 Å) and lb, WSe is the bond length of WSe with the value of (a +(c/8) ) / = 3.7 Å (a = 3.8 Å, c =.94 Å). 5. CHISHG as a nonlocal effect Interestingly, the observed phenomenon can be treated as a nonlocal effect that can be described by a nonlocal third order susceptibility tensor χ (3) ( ω, ω, ω, k ), where k z is the wave-vector (spatial frequency) of the applied DC field along the z direction. This tensor is equal to for k z =, i.e. for uniform DC and reaches maximum for the field that changes sign every half monolayer, i.e. when k = π / t.then one can obtain the SHG polarization as z xxxz z P = ε χ ( ω ; ω, ω, k ) E E ( k ) dk (3) x,ω xxxz, z x, ω z z z (3) But since the field can become non-uniform in the longitudinal direction only in the presence of space charge we prefer to call this phenomena charge-induced SHG. 5
6. An alternative explication of CHISHG There exists a different plausible explanation for the observed effect, and it has to do with the fact that bond orbitals in the bottom half-monolayer themselves lose the charge as holes accumulate near the surface. The density of the surface charge residing in the unoccupied bonds is estimated to be n = ε ( V V ) / ed 4.4 cm s ox T ox susceptibility of the scale of which is bound to engender second order χ ( n ) () xxx, b s ns () χ xxx, m nb. (4) where nb is the D density of the bonds. Therefore, the contribution of the second, direct accumulation charge contribution to the SHG is substantially less and can be neglected, compared to the charge-induced SHG. 7. Repeating charge-induced second-harmonic generation by using a femtosecond laser To clear the doubt of the sensitivities of CW laser used in our maintext, we have fabricated more devices and conducted SHG measurement with a femtosecond fibre laser excitation (pulse width of 69 fs, 9.4 nm center wavelength, MHz repetition rate, Model Origami-, Onefive GmbH). As shown in the plots below, the charge-induced second order optical susceptibility (the square root of SHG intensity) exhibit a threshold-like behaviour upon hole accumulation below - V, essentially the same with CW laser measurements (Fig. d in our revised manuscript), The only difference is that pulsed laser measurements show a very small non-zero χ () at positive bias (depletion region) that is orders of magnitude less than χ () accumulation region. This tiny χ () is almost independent on the applied voltage and is most probably a residual χ () due to imperfect H stacking in bilayer sample, as reported before (see Phys. Rev B, 87, 4, 3()). This supports our claim that charge induced SHG using CW laser can work as a noninvasive probe of future electronic devices. cm 5 in 6
I sd (µa) Charge-induced χ () (a.u.).5..5. 5 Log current I sd (A) -8 - -4-4 V G (V) -4-4 -4-4 V G (V) SHG intensity (a.u.) SHG intensity (a.u.) Slope =.97±.3. Excitation power (mw) 3 3 6 4 3 θ (deg) 8 Fig. S5. Charge-induced SHG measured by a femtosecond laser. (A) source-drain current (V sd =. V) with a back-gate sweep from -4 V to 4 V (inset, log-scale plot). (B) corresponding charge induced χ () at a femtosecond fibre laser with collimated ouput (mw used, MHz repetition rate, 69 fs, 9.4 nm center wavelength, Model Origami-, Onefive GmbH). (C) SHG intensity versus power showing an exponent of two (D)the polarization dependence under femtosecond laser excitation at V G = -3 V. 7
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